Shreyas holds 25 shares of a company at an average price of ₹150 and Vaishnavi holds 5 shares of the same company at an average price of ₹150.
- (i) Shreyas buys 10 shares of this company at a price of ₹30 each. What is the average price per share for him after the purchase?
- (ii) Vaishnavi buys some shares of this company at a price of ₹30 each and the average price per share for her after the purchase is ₹70. How many shares did she buy?
Step-by-step solution
Idea: The average price per share = total amount paidnumber of shares. Buying more shares at a lower price pulls the average down, more strongly when the new purchase is large compared with the old holding.
(i) Shreyas buys 10 shares of this company at a price of ₹30 each. What is the average price per share for him after the purchase?
- Amount paid: old 25 × 150 = ₹3750; new 10 × 30 = ₹300; total ₹4050 for 35 shares.1 mark
- Average price = 405035 ≈ ₹115.71.1 mark
(ii) Vaishnavi buys some shares of this company at a price of ₹30 each and the average price per share for her after the purchase is ₹70. How many shares did she buy?
- Let her buy n shares: 5 × 150 + 30n5 + n = 70, so 750 + 30n = 70(5 + n) = 350 + 70n.1 mark
- 400 = 40n ⇒ n = 10 shares.1 mark
Check: (ii): 750 + 30015 = 105015 = 70 ✓. Both bought 10 shares at ₹30, but Vaishnavi’s average fell much more (to ₹70) because her old holding was small (5 shares, against Shreyas’s 25).
Answer to write in the exam
(i)
Total cost = 25 × 150 + 10 × 30 = 3750 + 300 = ₹4050
Number of shares = 25 + 10 = 35
Average = 405035 = 115.71
∴ Average price ≈ ₹115.71 per share
(ii)
Let shares bought = n
5 × 150 + 30n5 + n = 70
750 + 30n = 350 + 70n
40n = 400 ⇒ n = 10
∴ She bought 10 shares
Common mistakes that cost marks
- Averaging the prices: 150 + 302 = ₹90. The numbers of shares at each price are different.
- In (ii), forgetting to add n to the number of shares in the denominator.
- Sign slips when solving 750 + 30n = 350 + 70n.
How this can come in the exam
Rina holds 20 shares at an average price of ₹100 and buys 20 more at ₹60 each. Her new average price is
- ₹70
- ₹80
- ₹90
- ₹160
Show answer
(B) ₹80
Equal numbers of shares: 100 + 602 = ₹80.
Arjun holds 12 shares at an average of ₹200. How many shares must he buy at ₹120 each to bring his average down to ₹150?
Show answer
2400 + 120n = 150(12 + n) (1 mark) ⇒ 2400 + 120n = 1800 + 150n ⇒ 30n = 600 ⇒ n = 20 shares (1 mark).Try one yourself
Meena holds 40 shares at an average price of ₹90 and buys 10 shares at ₹140 each. Find her new average price.
Show answer
3600 + 140050 = 500050 = ₹100.
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